Hit or Miss Sports is introducing a new product this year. If its see-at-night s

Question

Hit or Miss Sports is introducing a new product this year. If its see-at-night soccer balls are a hit, the firm expects to be able to sell 55,000 units a year at a price of $60 each. If the new product is a bust, only 35,000 units can be sold at a price of $55. The variable cost of each ball is $30, and fixed costs are zero. The cost of the manufacturing equipment is $6.5 million, and the project life is estimated at 10 years. The firm will use straight-line depreciation over the 10-year life of the project. The firm’s tax rate is 40%, and the discount rate is 10%.

Hit or Miss Sports can expand production if the project is successful. By paying its workers overtime, it can increase production by 30,000 units; the variable cost of each ball will be higher, however, equal to $35 per unit. By how much does this option to expand production increase the NPV of the project? (Assume the probability the see-at-night soccer balls will be a hit is 50%).

Hit or Miss Sports is introducing a new product this year. If its see-at-night soccer balls are a hit, the firm expects to be able to sell 55,000 units a year at a price of $60 each. If the new product is a bust, only 35,000 units can be sold at a price of $55. The variable cost of each ball is $30, and fixed costs are zero. The cost of the manufacturing equipment is $6.5 million, and the project life is estimated at 10 years. The firm will use straight-line depreciation over the 10-year life of the project. The firm’s tax rate is 40%, and the discount rate is 10%.

Hit or Miss Sports can expand production if the project is successful. By paying its workers overtime, it can increase production by 30,000 units; the variable cost of each ball will be higher, however, equal to $35 per unit. By how much does this option to expand production increase the NPV of the project? (Assume the probability the see-at-night soccer balls will be a hit is 50%).

Explanation / Answer

- Expected units sold = (55,000 x 0.5) + (35,000 x 0.5) = 45,000 units

- Expected selling price = (60 x 0.5) + (55 x 0.5) = $57.5 per unit

- Depreciation per year = 6,500,000 / 10 = $650,000

Normal Case:

Subsequent Annual Cash Inflows = [45,000 x (57.5 - 30) - 650,000] x (1 - 0.40) + 650,000 = $1,002,500

NPV = -6,500,000 + 1,002,500 x PVAF(10%, 10years) = -6,500,000 + 1,002,500 x 6.145 = -$340,071.48

If Overtime is paid:

Subsequent Annual Cash Inflows = [75,000 x (57.5 - 35) - 650,000] x (1 - 0.40) + 650,000 = $1,272,500

NPV = -6,500,000 + 1,272,500 x PVAF(10%, 10years) = -6,500,000 + 1,272,500 x 6.145 = $1,318,961.64

Increase in NPV = 1,318,961.64 - (-340,071.48) = $1,659,033.12

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